Next: Complex Arithmetic, Up: Arithmetic [Contents][Index]

### 17.1 Exponents and Logarithms

: exp (x) ¶

  Compute `e^x` for each element of x.

  To compute the matrix exponential, see Linear Algebra.

  See also: log.

: expm1 (x) ¶

  Compute `exp (x) - 1` accurately in the neighborhood of zero.

  See also: exp.

: log (x) ¶

  Compute the natural logarithm, `ln (x)`, for each element of x.

  To compute the matrix logarithm, see Linear Algebra.

  See also: exp, log1p, log2, log10, logspace.

: reallog (x) ¶

  Return the real-valued natural logarithm of each element of x.

  If any element results in a complex return value `reallog` aborts and issues an error.

  See also: log, realpow, realsqrt.

: log1p (x) ¶

  Compute `log (1 + x)` accurately in the neighborhood of zero.

  See also: log, exp, expm1.

: log10 (x) ¶

  Compute the base-10 logarithm of each element of x.

  See also: log, log2, logspace, exp.

: y = log2 (x) ¶
: [f, e] = log2 (x) ¶

  Compute the base-2 logarithm of each element of x.

  If called with one output, compute the base-2 logarithm such that `2^y = x`.

  If called with two output arguments, split x into binary mantissa (f) and exponent (e) such that `x = f * 2^e` where `1/2 <= abs (f) < 1` and e is an integer. If `x = 0`, `f = e = 0`.

  See also: pow2, log, log10, exp.

: pow2 (x) ¶
: pow2 (f, e) ¶

  With one input argument, compute 2 .^ x for each element of x.

  With two input arguments, return f .* (2 .^ e).

  See also: log2, nextpow2, power.

: n = nextpow2 (x) ¶

  Compute the exponent for the smallest power of two larger than the input.

  For each element in the input array x, return the first integer n such that 2^n ≥ abs (x).

  See also: pow2, log2.

: realpow (x, y) ¶

  Compute the real-valued, element-by-element power operator.

  This is equivalent to `x .^ y`, except that `realpow` reports an error if any return value is complex.

  See also: power, reallog, realsqrt.

: sqrt (x) ¶

  Compute the square root of each element of x.

  If x is negative, a complex result is returned.

  To compute the matrix square root, see Linear Algebra.

  See also: realsqrt, nthroot.

: realsqrt (x) ¶

  Return the real-valued square root of each element of x.

  If any element results in a complex return value `realsqrt` aborts and issues an error.

  See also: sqrt, realpow, reallog.

: cbrt (x) ¶

  Compute the real-valued cube root of each element of x.

  Unlike `x^(1/3)`, the result will be negative if x is negative.

  If any element of x is complex, `cbrt` aborts with an error.

  See also: nthroot.

: nthroot (x, n) ¶

  Compute the real (non-complex) n-th root of x.

  x must have all real entries and n must be a scalar. If n is an even integer and x has negative entries then `nthroot` aborts and issues an error.

  Example:

      nthroot (-1, 3)
      ⇒ -1
      (-1) ^ (1 / 3)
      ⇒ 0.50000 - 0.86603i

  See also: realsqrt, sqrt, cbrt.

Next: Complex Arithmetic, Up: Arithmetic [Contents][Index]